Low-pass filters and representations of the Baumslag Solitar group

Details Low-pass filters and representations of the Baumslag Solitar group Low-pass filters and representations of the Baumslag Solitar group

2004-07-20

arxiv.org/abs/math/0407344v3

Trans. Amer. Math. Soc. 358 (2006), no. 12, 5271--5291

Mathematics

Classical Analysis and ODEs

Scientific paper

We analyze representations of solvable Baumslag Solitar group that admit wavelets and show how such representations can be constructed from a given low-pass filter. We describe the direct integral decomposition for some examples and derive from it a general criterion for the existence of solutions for scaling equations. As another application, we construct a Fourier transform for some Hausdorff measures.

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